8.3.1 Definite integrals and areas Quiz: Pearson Edexcel Maths, Unit 8

The 20 questions

1. What does the definite integral of a function represent geometrically?

   • Average gradient
   • Total length
   • Signed area
   • Maximum value

2. Which calculus theorem links definite integration to antidifferentiation?

   • Remainder theorem
   • Fundamental theorem
   • Mean value theorem
   • Binomial theorem

3. How do you calculate the total physical area bounded between a curve and the x-axis?

   • Split intervals
   • Square the function
   • Double the integral
   • Ignore negative signs

4. What is the integral from 4 to 4 of x cubed dx?

   • 256
   • 64
   • 16
   • 0

5. Which integration property allows splitting the integral from a to c into a to b plus b to c?

   • Symmetry
   • Linearity
   • Additivity
   • Homogeneity

6. What does reversing the upper and lower limits of a definite integral do to its value?

   • Negates it
   • Squares it
   • Halves it
   • Has no effect

7. What is the value of the definite integral from 0 to pi of sin x dx?

   • 0
   • 2
   • 1
   • pi

8. What is the area enclosed between the curves y = x squared and y = x?

   • 1/3
   • 1/4
   • 1/2
   • 1/6

9. What expression gives the area between a curve y = f(x) and the y-axis from y = c to y = d?

   • Integral y dx
   • Derivative x dy
   • Integral x dy
   • Integral f(x) dx

10. Evaluate the definite integral from 1 to e of 1/x dx.

    • 1
    • ln(e)
    • e
    • 0

11. What is the definite integral from -2 to 2 of x cubed dx?

    • 4
    • 16
    • 0
    • 8

12. What is the exact value of the integral from 0 to 1 of e to the power of 2x dx?

    • 0.5(e squared - 1)
    • 2(e squared - 1)
    • e squared
    • e squared - 1

13. Which rule is used when a substitution is applied to the limits of a definite integral?

    • Change limits
    • Keep original limits
    • Invert the limits
    • Square the limits

14. What is the value of the definite integral from 0 to 0.5 of 1 over root(1 - x squared) dx?

    • pi / 6
    • pi / 3
    • pi / 2
    • pi / 4

15. What is the area of the region bounded by y = 4 - x squared and the x-axis?

    • 8/3
    • 16/3
    • 32/3
    • 64/3

16. What does a negative value for a calculated area between two curves usually indicate?

    • Asymptotic limit
    • Correct answer
    • Incorrect setup
    • Symmetric region

17. What is the integral from 1 to 2 of 3 over x squared dx?

    • 0.75
    • 3
    • 2.25
    • 1.5

18. Which definite integral represents the total accumulated distance travelled by a velocity function v(t)?

    • Integral v'(t) dt
    • Integral |v(t)| dt
    • Integral v(t) dt
    • Derivative v(t) dt

19. What is the value of the definite integral from -1 to 1 of x to the power of 4 dx?

    • 1/5
    • 2/5
    • 2/3
    • 0

20. What is the exact value of the definite integral from 0 to 1 of 3x squared dx?

    • 0
    • 1
    • 9
    • 3

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